Prime p₀= 1588518915115989971 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 118 2 16 2 40 2 16 2 (?)
a_n: 0 2 30 32 48 50 168 170 186 188 228 230 246 248
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 248
Found by: Theadalus
db: batch=78, k=14, 28 16 118 16 40 16

SPT(16)	1588518281032322477	0 12 26 50 56 122 126 146 180 200 204 270 276 300 314 326	-634083667494
SPT(16)	1588518291551265637	0 34 40 66 84 96 112 124 252 264 280 292 310 336 342 376	-623564724334
TPT(14)	1588518326810078117	0 2 54 56 60 62 84 86 102 104 114 116 354 356	-588305911854
STPT(10)	1588518342677855987	0 2 30 32 72 74 114 116 144 146	-572438133984
SPT(16)	1588518662751876113	0 20 60 90 104 110 146 170 240 264 300 306 320 350 390 410	-252364113858
STPT(10)	1588518807744274379	0 2 30 32 120 122 210 212 240 242	-107371715592
SPT(16)	1588518988616043623	0 44 54 86 90 128 168 200 294 326 366 404 408 440 450 494	73500053652
SPT(16)	1588519137467360327	0 36 42 60 104 146 164 194 342 372 390 432 476 494 500 536	222351370356
TPT(14)	1588519305635366009	0 2 48 50 138 140 318 320 402 404 432 434 462 464	390519376038
STPT(10)	1588519977724129997	0 2 30 32 42 44 54 56 84 86	1062608140026
STPT(10)	1588520005055943917	0 2 60 62 72 74 84 86 144 146	1089939953946